Stability analysis of one-dimensional steady cavitating nozzle flows with bubble size distribution

A continuum bubbly mixture model coupled with the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A bubbly liquid with a distribution of nuclei sizes is flowing through a nozzle. The upstream cavitation number and the minimum or throat pressure coefficient are chosen so that cavitation occurs in the flow. Computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the quasi-static flow. For example, the energy density distribution in the flow demonstrates that the presence of multiple-sizes bubbles reduces the downstream fluctuation and therefore reduces the 'cavitation loss'. Another interesting interaction effect is that flashing instability occurs as the flow reaches some critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and the numerical results for flows of both equal bubble size and multiple bubble sizes.